Dynamic readout of the Hh gradient in the Drosophila wing disc reveals pattern-specific tradeoffs between robustness and precision

Understanding the principles underlying the design of robust, yet flexible patterning systems is a key problem in developmental biology. In the <i>Drosophila</i> wing, Hedgehog (Hh) signaling determines patterning outputs using dynamical properties of the Hh gradient. In particular, the pattern of <i>collier</i> (<i>col</i>) is established by the steady-state Hh gradient, whereas the pattern of <i>decapentaplegic</i> (<i>dpp</i>), is established by a transient gradient of Hh known as the Hh overshoot. Here, we use mathematical modeling to suggest that this dynamical interpretation of the Hh gradient results in specific robustness and precision properties. For instance, the location of the anterior border of <i>col</i>, which is subject to self-enhanced ligand degradation is more robustly specified than that of <i>dpp</i> to changes in morphogen dosage, and we provide experimental evidence of this prediction. However, the anterior border of <i>dpp</i> expression pattern, which is established by the overshoot gradient is much more precise to what would be expected by the steady-state gradient. Therefore, the dynamical interpretation of Hh signaling offers tradeoffs between robustness and precision to establish tunable patterning properties in a target-specific manner.